2. A factory produces two types of products. To produce these products, the factory needs some...

 

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2. A factory produces two types of products. To produce these products, the factory needs some resources, such as labor and two raw materials (i.e., aluminum and glass). The factory has available four different machines to produce these two products; each machine uses various amounts of labor and two raw materials. The inputs and outputs for 1 hour of each of the four machines are given in the following table. Machine. Labor (hours) 20 C. Input Aluminum (kg) 160 Glass (kg) 30 35 100 200 75 Product 1 (units) 35 Output X, 1 42 2 30 45 √3 10 60 0 70 14 4 25 80 0 90 The factory is responsible to produce 2100 units of Product 1 and 1800 units of Product 2 each week. However, it has limited resources. Each week, the factory only has 8 tons of aluminum, 4 tons of glass, and 1000 hours of labor. Per kg of aluminum and glass cost for $3 and $7, respectively. Because of labor contracts, the plant must pay its employees a full week's salary, regardless of whether or not the employees are used that week, so the cost of the 1000 hour of labor is fixed. (Hint: there are 4 decision variables) Product 2 (units) 55 42 a. Formulate an LP model to use the four machines to minimize the total cost. b. If the factory manager allows his workers to work up to an extra 200 hours per week in overtime at a cost of $30/hour. What will be the LP model by considering this overtime possibility? From the model you have made in 2.a., change it into an LP standard form. .... 2. A factory produces two types of products. To produce these products, the factory needs some resources, such as labor and two raw materials (i.e., aluminum and glass). The factory has available four different machines to produce these two products; each machine uses various amounts of labor and two raw materials. The inputs and outputs for 1 hour of each of the four machines are given in the following table. Machine. Labor (hours) 20 C. Input Aluminum (kg) 160 Glass (kg) 30 35 100 200 75 Product 1 (units) 35 Output X, 1 42 2 30 45 √3 10 60 0 70 14 4 25 80 0 90 The factory is responsible to produce 2100 units of Product 1 and 1800 units of Product 2 each week. However, it has limited resources. Each week, the factory only has 8 tons of aluminum, 4 tons of glass, and 1000 hours of labor. Per kg of aluminum and glass cost for $3 and $7, respectively. Because of labor contracts, the plant must pay its employees a full week's salary, regardless of whether or not the employees are used that week, so the cost of the 1000 hour of labor is fixed. (Hint: there are 4 decision variables) Product 2 (units) 55 42 a. Formulate an LP model to use the four machines to minimize the total cost. b. If the factory manager allows his workers to work up to an extra 200 hours per week in overtime at a cost of $30/hour. What will be the LP model by considering this overtime possibility? From the model you have made in 2.a., change it into an LP standard form. ....

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